Abstract
In this paper, we analyze the electrostatic charge distribution on arbitrarily shaped conductor surfaces. Following a perturbative approach, we derive an approximate analytical formulation of the problem. We start from the known case of a conducting ellipsoid, we adopt a deformed ellipsoidal coordinate system, and we search for the zero-order approximated solution of the problem. We also focus on arbitrary-shaped thin foils, showing that the charge density is divergent on their borders. We then define the applicability range of the proposed approach expressing the contour equation as the Fourier series. Finally, we present a detailed error analysis for several polygonal contours, comparing the analytical results with those obtained via a numerical analysis based on the Finite Element Methods (FEM).
Highlights
The problem of finding the electrostatic charge distribution on a charged conductor is a fascinating problem that many classical electrodynamics textbooks solve in several analytical cases [1]–[3]
ELECTRICAL POTENTIAL GENERATED BY A CONDUCTOR SURFACE Our goal is to find an analytical solution of
In this paper, we presented an analytical formulation of the problem of electrostatic charge distributions on arbitrarily shaped conductor surfaces
Summary
The problem of finding the electrostatic charge distribution on a charged conductor is a fascinating problem that many classical electrodynamics textbooks solve in several analytical cases [1]–[3]. Several practical problems are related to the identification of the charge distribution and possibly its optimization, on thin surface domains, for instance, in energy harvesting and designing devices [10], [11], semiconductors [12], photovoltaics, and optoelectronics [13], [14]. In electrical accumulators, such as lithium batteries, the study of the charge density distribution has a crucial role in developing new techniques to reduce dendrite growth [15], [16]. The knowledge of the charge distribution of a generic geometry of the conductor can allow for a better designing the conductor geometries and for reducing the possibility of occurrence of electrostatic discharge [17]–[19]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
